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"Painting with a broad brush" probably began as an analogy, but once enough people use it, it becomes an idiom. If understanding is shared between speaker/writer and listener/reader, idioms are a useful shorthand for sharing some commonly understood argument.
So useful, in fact, that people often forget what the original analogy was. For example, the verb "rewind." How many people using it think of reel-to-reels, cassettes, or videotapes?
http://learnersdictionary.com/qa/Idioms-metaphors-similes-an....
>A common antipattern here in HN comments is someone using an analogy (which is almost always bad), and then the responses devolving into arguing over how the analogy isn't correct.
That statement is too broad to possibly be true.
Analogies... are more pernicious than you think.
Indeed, if one wishes to be extremely extreme, one might go as far as to argue that all language is ‘analogy’, insofar as it assigns symbolic monikers to real-world objects. Furthermore, phonetic encodings (alphabets) are a further level of analogy, as they posit that (for example) the “in” in “indeed” is “similar enough” to the “in” in “insofar” to be denoted with identical symbols. Those symbols are, themselves... you guessed it... analogies, metaphors, and other various kinds of abstractions.
I honestly think a "no analogies" rule for commenting would do more to facilitate good discussion than the existing "no jokes" rule. Analogies are almost never useful. Even the ancient Greeks realized this.